Fluctuations of Levy Processes with Applications: Introductory Lectures - Universitext (Paperback)Andreas E. Kyprianou (author)
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Levy processes are the natural continuous-time analogue of random walks and form a rich class of stochastic processes around which a robust mathematical theory exists. Their application appears in the theory of many areas of classical and modern stochastic processes including storage models, renewal processes, insurance risk models, optimal stopping problems, mathematical finance, continuous-state branching processes and positive self-similar Markov processes.
This textbook is based on a series of graduate courses concerning the theory and application of Levy processes from the perspective of their path fluctuations. Central to the presentation is the decomposition of paths in terms of excursions from the running maximum as well as an understanding of short- and long-term behaviour.
The book aims to be mathematically rigorous while still providing an intuitive feel for underlying principles. The results and applications often focus on the case of Levy processes with jumps in only one direction, for which recent theoretical advances have yielded a higher degree of mathematical tractability.
The second edition additionally addresses recent developments in the potential analysis of subordinators, Wiener-Hopf theory, the theory of scale functions and their application to ruin theory, as well as including an extensive overview of the classical and modern theory of positive self-similar Markov processes. Each chapter has a comprehensive set of exercises.
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Number of pages: 455
Weight: 7139 g
Dimensions: 235 x 155 x 24 mm
Edition: 2nd ed. 2014
"The book grew out of lectures pitched at an advanced undergraduate or beginning graduate audience, the prerequisite being a course on abstract Lebesgue integration and a good foundation in probability theory ... . Fluctuations of Levy processes is an interesting book and it is currently the best introduction for the novice to this important topic." (Rene L. Schilling, Mathematical Reviews, April, 2015)
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